Abstract
In this paper, we study the relation between the discrete and the continuous mean values of $\Delta_a^2(x)$, where $\Delta_a(x)$ $(-1<a<1)$ is the error term in the generalized divisor problem. We try to find the formula of the difference of these mean values in a sufficiently explicit form. As an application we give the asymptotic formula of the discrete mean square of $\Delta_a(n)$ in the range $-1<a<1, a\not=0$. We also study the integral containing the error term in the weighted two-dimensional divisor problem.
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